We obtain some properties of a class of $q$-hypergeometric orthogonal polynomials with $q=-1$, described by a uniform parametrization of the recurrence coefficients. We show that our class contains the Bannai-Ito polynomials and other known -1 polynomials. We introduce some new examples of -1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra.
Hypergeometric orthogonal polynomials of Jacobi type
Additions to the formula lists in "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw
Dunkl shift operators and Bannai-Ito polynomials
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